I'm not able to paste InDesign elements into Photoshop

Can not right click the element in InDesign, and choose Edit Original?  If it is a a file type associated with Photoshop, it should open up in Photoshop.  Once it is in Photoshop you save any edits and they will link back to InDesign, but you can also treat it as a separate object and Save As to your hard drive etc.  You can do the same thing with Smart Objects in Photoshop.  When you double click to open an SO in a new window, that will have the PSB format, you can save it as a PSD to make it a new document in its own right.

I'd also look at using CC Libraries.  They are incredibly useful for inter-app asset use, and have the advantage that you can create a named library for specific projects, or clients.  I love being able go straight to the relevant Library to find fonts, brushes, colour swatches, Smart Objects etc. all in one convenient location, that I can find from whatever system I happen to be using.  This is so much more convenient than looking for, and opening previous projects to find the same information.

If you're trying to copy/paste text, that does not work well.

If you're trying to copy/paste elements other than text, you can do that. When you paste into Photoshop, the elements will be pasted in a separate Smart Object layer. You will not be able to edit the individual elements within that layer. Theoretically, if you want to edit you should be able to double-click on the layer to open it in InDesign and edit it, but Photoshop will usually try to open it in Acrobat instead.

Providing the elements are not text, it works better to copy/paste into Illustrator, then copy/paste from Illustrator into Photoshop.

¿Do you get some message or error? Usually, is possible copy-paste InDesign elements into Photoshop but those elements are rasterized. You can try exporting those elements from InDesign and opening it in Photoshop.

What kind of "elements", specifically?